How do you write #y = | x - 2|# as piecewise functions?

2 Answers
Dec 26, 2017

Answer:

See a solution process below:

Explanation:

Step 1) First, solve the term within the absolute value function for #0#:

#x - 2 = 0#

#x - 2 + color(red)(2) = 0 + color(red)(2)#

#x - 0 = 2#

#x = 2#

Step 2) Multiply the term within the absolute value function by #-1# and write a "less than" inequality with the result of Step 1:

#-1(x - 2) => -x + 2#

#y = -x + 2" for "x < 2#

Step 3) Take the term within the absolute value function and write a "greater than or equal to" inequality with the result of Step 1:

#y = x - 2" for "x >= 2#

Step 4) Combine Step 2 & Step 3 to form the piecewise function:

#y = {-x + 2" for "x < 2; x - 2" for "x >= 2}#

Dec 26, 2017

Answer:

see below

Explanation:

#f: y=|x−2|#


#f_1: y=x#
#f_2: y=|x|#
#f_3: y=|x-2|#

Absolute value mirrors every negative value to the positive according to x axis.
And finally, a number inside absolute value moves graph to the right or left. When it's minus:#|x-2|# then it moves to the right. You can remember it by finding zero point, which is 2 and it's greater than zero(on the right from zero). Now you should be able to make a graph
enter image source here